Prove the following by using the principle of mathematical induction for all

Let P(n):
I.         For n = 1,
         P(1) :

∴       P(1) is true.
II.      Suppose the statement is true for n = m,
         P(m):      ...(i)
III.     For n = (m + 1),
         P(m + 1) :
or       
      From (i),
        

∴  




         Which is true

∴        P(m + 1) is true

∴        P(m) is true P(m + 1) is true
Hence, by the principle of mathematical induction, statement P(n) is true for all